"publicity or press agent," 1945, also by that year as a verb, said to have been coined at show biz magazine "Variety" (but the first attested use is not in "Variety") and supposedly from name of Gene Flack, a movie agent, but influenced by flak. There was a Gene Flack who was an advertising executive in the U.S. during the 1940s, but he seems to have sold principally biscuits, not movies.